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On the local meromorphic extension of CR meromorphic mappings

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Merker J., Porten E.

Annales Polonici Mathematici

1998

tom 70

nr 1

163-193

Let M be a generic CR submanifold in $ℂ^{m+n}$, m = CR dim M ≥ 1, n = codim M ≥ 1, d = dim M = 2m + n. A CR meromorphic mapping (in the sense of Harvey-Lawson) is a triple $(f,𝓓_f,[Γ_f])$, where: 1) $f: 𝓓_f → Y$ is a 𝓒¹-smooth mapping defined over a dense open subset $𝓓_f$ of M with values in a projective manifold Y; 2) the closure $Γ_f$ of its graph in $ℂ^{m+n} × Y$ defines an oriented scarred 𝓒¹-smooth CR manifold of CR dimension m (i.e. CR outside a closed thin set) and 3) $d[Γ_f] = 0$ in the sense of currents. We prove that $(f,𝓓_f,[Γ_f])$ extends meromorphically to a wedge attached to M if M is everywhere minimal and $𝓒^ω$ (real-analytic) or if M is a $𝓒^{2,α}$ globally minimal hypersurface.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Merker J.

1 Porten E.

1 1998

Wyniki wyszukiwania

On the local meromorphic extension of CR meromorphic mappings